OFFSET
1,2
COMMENTS
Numbers n such that n + (0, 4) is a prime power pair.
A generalization of the cousin primes. The cousin primes are a subsequence.
n + (0, 2m), m >= 1, being an admissible pattern for prime pairs, since (0, 2m) = (0, 0) (mod 2), has high density.
n + (0, 2m-1), m >= 1, being a non-admissible pattern for prime pairs, since (0, 2m-1) = (0, 1) (mod 2), has low density [the only possible pairs are (2^a - 2m-1, 2^a) or (2^a, 2^a + 2m-1), a >= 0.]
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1256 from Daniel Forgues)
MATHEMATICA
Select[Range[1000], PrimeNu[#] < 2 && PrimeNu[# + 4] < 2 &] (* Amiram Eldar, Oct 01 2020 *)
PROG
(PARI) is(n)=if(n==1, return(1)); isprimepower(n) && isprimepower(n+4) \\ Charles R Greathouse IV, Apr 24 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Daniel Forgues, Aug 16 2009, Aug 17 2009
STATUS
approved